Blind vs. Blind, Take 2

Ah, the power of the Internet. I received a handful of email responses and one anonymous comment about a recent blog post in which I claimed a big blind should essentially defend with 100% of their range when facing a 3x small blind open (click here to read that original post).

Turns out I was wrong in that post. Let me explain... or, better, I'll let the anonymous commenter explain:

"Your goal is not to be profitable with your whole range, your goal is to be as profitable as possible. This means calling only with hands that individually have enough equity. So you should fold hands like 74o which only has 32.35% equity."

He (or she) (and all the emailers, too) correctly pointed out that running a hero range against villain's range is silly. What actually matters are individual specific hands played against villain's range; i.e., I'm not playing a range of hands from the big blind, I'm playing a single specific hand. In other words, each single hand has to have at least 33% pot equity by itself against the villain's range to make calling a break even play with that hand.

So, that's exactly what I did-- I ran my equity calculator a whole slew of times with individual hands against the villain's range. I kept track of which hands had greater than 33% equity, and then plotted them on a card matrix. Here's my new, corrected defending range from the big blind:

Again, don't take the wrong message from this. For example, I'm pretty sure I wouldn't actually always defend with Q5o or K3o when facing a SB open; these kinds of hands have only slightly higher than 33% equity, and are generally quite difficult to play postflop; they could end up actually costing you money in the long run unless you play them perfectly. In other words, it's a pretty close decision with a lot of the hands that the matrix indicates are playable...

....but the bottom line message is still clear: the range of hands that you can/should defend with is pretty damn wide.

Thanks to all you who sent me comments. I really appreciate all y'all settin' me straight.

All-in for now...
-Bug

Blind vs. Blind

Here's a weird one I discovered while noodling around with a new equity calculator I downloaded recently*. The result I get is strange enough that I'm actually not fully convinced it's true. If you see a flaw in my math or logic, please email or leave a comment:

Scenario: You're in the Big Blind and the action folds all the way 'round to the Small Blind. He's a regular ABC TAg player, and he opens to 3x.

Question: From a theoretical math point of view, how often should you call?

Short Answer: A lot.

Longer Answer: A helluva lot.

Here's Why: For argument's sake, let's assume that the SB is not opening crazy wide. Call it all Broadways, all Pocket Pairs, and all Aces. This is just under 28% of hands (366/1326), and this is what it looks like in a card matrix:

When the villain opens to 3x, there is 4x in the pot (his 3x open, plus your 1x big blind). It's going to cost you 2x more to call, so you're getting 2:1 direct pot odds. This means you need 33% pot equity to breakeven if you were to call and the hand runs out hot-and-cold to the river (1/(2+1)). If your pot equity is higher than this, it's profitable to call; if it's lower, than it's not profitable.

In terms of range, what does 33% equity look like against villain's opening range? My assumption is that I'm re-raising the top 15% of my range (all but the worst Broadways, and 77+). Everything else is fair game to just call with. So I started opening up a range of hands against Villain's range in Equilab...

... and I was pretty shocked when I ran the numbers. I basically kept adding cards, trying to drive my equity down to 33%. Turns out I couldn't. The closest I could get was 35%, and that is with this range:

Yep, this means when I'm not 3betting the premium hands, I should be calling. Period. Yep, all 100% of my range. Yep, seriously. And it gets even more pronounced with opening up Villain's range wider. Seriously. For instance, if Villain opens with, say, 35% of his hands, I automatically get about 38% equity with any two cards. Change his range to a LAggy 50% range, and my equity jumps to 42% with any tow random cards. And so on...

Now, this is the theoretical math solution. The reality is that I would be psychologically hard pressed to call with total junk hands like K3o and the like, as they're actually pretty hard to play post-flop, even in position. (Remember: this exercise assumes all post-flop action is moot, and the hands run hot-and-cold to the river as-is.) But still... this is pretty amazing.

Another wrong message to take from this example is to start defending your blinds lightly against button openers. You'll be OOP throughout the hand, which will have a serious impact on your ability to play postflop poker. You'll need more equity than just 33% to make defending against a button steal.

Anyway, I found this fairly interesting... but like I said, I'm not convinced I didn't do something dumb along the way in my analysis. Any and all comments are welcome!

All-in for now...

-Bug

*PokerStove does not seem to be available for download anymore. That's the bad news. The good news is there's an equally good (and still free) program that does what PS did (actually the new software does more). The program is called Equilab, and it's created/provided by Pokerstrategy.com. Click here for the link to download it.

to Defend, or not to Defend. that is the Question.

While waiting for my computer to finish a big synch before I jump back into work tonight, I surfed to the hand of the day. As it's been a while since I tackled one of these, I decided to give it a go:

My standard method to tackle poker hand analyses is--big surprise--REDi. While this method works great for cash games, I'm still tweaking the method for MTT play and I'm not 100% sure it's perfected yet for tournament play. I have to find a way to fold in opp stack sizes and their commitment level. Here's a stab at including that part of the Read into the process:

Reads: What's a little strange about this hand is the statement that your opponent has been "raising about 20% from late position." If this were a cash game, I'd start with that approximate VPIP and evaluate my hand against that range. Ah, but this is a tournament, and we have to put ourselves in the head of the villain, given the size of his chip stack relative to the blinds and antes.

Before raising, the villain had about 15.5 big blinds, which isn't horrible, but the antes have kicked in and his M = 6276 / ((9x50)+200+400) = approximately 6. This is a little more serious. If the opp is worth his salt (and he should be halfway through a $100 large field online MTT) he has to realize his growing desperation. In other words, he should be shoving with his entire range. But he's not. Why? He has to know that he's seriously hurting his stack if we 3bet and he folds to the re-raise here (his M will drop to under 5).... so he's probably not going to fold. Adding to this read on him is that our own image is "aggressive," which means he knows we're likely to re-steal out of the blinds against a weak stack. This in turn means his range is actually probably tighter than the 20% stated in the problem. In other words, it feels like he wants a re-raise.

Putting all this together, I would err on the side of caution, and put him on 88+, AQo+, and KQs. 

Evaluate:

• Against this range, our KQs is a 2:1 dog.
• Even if we make his range 22+, AJo+, and KQo+, our equity is just 41%, which is a long way from a coin flip.
• We're not pot committed.
• We have a non-desperate M.
• We have the big blind yet to act after us.
• We have very little fold equity.
• If we call, we'll be OOP with trap hand.

Decide: I don't see why we want to do anything but fold and wait for a better, lower risk opportunity to build our stack. If our hand was AKs, our equity would be significantly higher (~50-55%), which would make this a much easier call. But when we have significantly less than 50% equity, we're not committed, and what we stand to gain helps us less than what we stand to lose, this seems like an easy fold.

Implement: Fold.

All-in for now...

-Bug